That's a mold, with 2 external parts and a core. The exterior prints wonderful. But the core is too messy. Take a look at this:

What riddles me is that the side parts, and the pole's base, print fine; so this does not look like a bad calibrated printer, but something else entirely. My guess is this is some precise tuning I don't know yet.

I've been trying to print that little pole without success for over a week now. Tried all this:

Changing the slicer program (I've used Ultimaker Cura and Slic3r prusa edition)

Tuning the e-steps for avoiding over-extrusion.

Tuning the z-steps, so the nozzle doesn't melt the last layer when printing a new one.

So far, the best I got is a little pole not-too-deformed so I can make my part anyway, even when the pole is not well printed. But after seeing lots of videos and reading lots of tips online, I still don't understand how to tune my print for that simple little pole.

Other that tips, what I would really like to ask is if somebody has a name for that problem I'm facing, so it would be much more easy to search for my tuning options.

$\begingroup$Try printing it at 1/10 the speed that you normally do, or switch to a smaller nozzle, re-slice, then try again. What material are you printing in?$\endgroup$
– user77232Mar 25 '19 at 4:51

When printing a series of small parts, print them all together. The
travel time between the parts is often enough time for the layers to
cool without changing your settings.

If you do want this to print as a single piece, you need to:

tune down hotend temperature (use the minimum temperature that gives good print results, printing a temperature tower will help to determine this),

increase minimal layer time (may not always work as speed will not be lowered under the minimum printing speed) and

increase part cooling fan percentage (or print a better fan duct that allows for more cooling air to reach the print; many fan ducts are too convergent, the pressure increase is then too big for the fan to effectively push air through it).

The other answers have addressed the heat problem. The other risk is that a rod printed vertically like this is prone to snap, because the weakest axis is between layers.

I often rotate pieces like this and print with the rod horizontal. You then have to remove the support and/or brim material, and probably do a bit of sanding to get it properly round, but the final part will be much more reliable (not break).

$\begingroup$Yes strength can be a problem, I've printed such parts with room for a screw to strengthen the part. But if that is not possible, a change in print orientation might be very helpful!$\endgroup$
– 0scar♦Mar 26 '19 at 7:17

The thin core gathers too much heat in the printing process. If you need to print slender objects, either:

Print several. This is the most simple solution and best for beginners.

Increase cooling. A better cooling solution or increased fan speed often can help to get thin or delicate objects printed.

set minimum layer time to slow down the printer automatically on layers with low cross-sections. If too small, it could pause on the edge of the print, which could leave scorch marks.

If you know a little more about your printer and got your retraction dialed in, you can go more advanced: set minimum layer time to 10 to 15 seconds and activate the accompanying Z-hop. This will prevent the scorch marks, but you might need to make sure you don't string.

$\begingroup$Although you are correct, adding Z-hop introduces the chance of a leaking/oozing hotend or filament not being extruded in time, that would not be my personal preferred solution for people starting using 3D printers for the first time.$\endgroup$
– 0scar♦Mar 26 '19 at 7:14

I'm sorry for the long time I took to answer, but the ammount of NEW problems I faced since started this question was so big that wanted to write a list of them before answering my own question. I've finally also desisted from the list, as the problems tends towards infinity.

Simple version: printing more than a single item did the trick, as several people proposed here. But then the piece broke when tried to remove it from the hot bed, as somebody else also warned me here. By that time I tried a temp tower, had to recalibrate almost the whole printer, had to also relubricate it, had to learn some tricks about sticking and de-sticking pieces from the bed, tried several different glues, started to fine-tune my slicings, and so on and so on... man, 3D printing is laborious.

But I wanted to let this link here for all the fellow newbies out there reading this.